Abstract Using a game-theoretic analysis, this study aims to investigate which of the “all or nothing” and “pro rata” methods, regarding the sanction against the breach of duty to disclose in insurance contracts by negligence, is better from two perspectives: one is in terms of how much the sanction increases the policyholder’s probability of effort, while the other is how much it increases the probability of finding the wrong type of policyholder by insurance firms. From the analysis, we find that the desirable method depends on the probability that the policyholders can effortlessly determine their precise risk type as well as their effort cost level.

This study examines whether the introduction of compulsory bicycle liability insurance is socially desirable when evaluation bias—the difference between the objective and subjective evaluations of liability amounts—exists. The main results of this study are summarized as follows. First, when there is no evaluation bias, the introduction of compulsory bicycle liability insurance is socially desirable when the interest rate is high without any condition, and the loading rate is low, the maximum amount of liability is small, and the effort cost is high if the loading rate is higher than the interest rate. Second, if there is an evaluation bias and the accident probability is uniformly distributed, more severe additional conditions are needed for deriving the same results. The study concludes that the evaluation bias prevents the realization of the situation in which the introduction of compulsory bicycle liability insurance is socially desirable.